Question

Volume of Shaded area on a cylinder??
It Height is 11in.
base is 5in.

Answer 1

This is what the cylinder looks like.
Please help. I'm studying for my final on Weds.

Answer 2

It's the volume of the cylinder minus the volume of the cone inside it. Formulas you need to use: \(\LARGE V_{cylinder} = \pi r2h \) and \(\LARGE V_{cone} = \frac{\pi r^3 \sqrt{3}}{3} \)

Answer 3

And area of the base is pi*r^2.

Answer 4

On a note, I was mistaken about the cone volume, it should be \(\LARGE \frac{1}{3} BH\) You have base and height.

Answer 5

Thank you! But how do I find the Radius for the Volume of the Cylinder?

Answer 6

Ok, let me reformulate this because it got messy. I assume that you have the diameter of the base (it's in inches, if it was the area, it had to be in inches squared). So radius = diameter/2 = 2.5. So, the volume of the cylinder is straightforward: pi*((2.5)^2)*(11) = 216 in. cubic. Now, onto the cone: divide the volume of the cylinder by 3 (same height, same base), we get: 72. Volume of the shaded region is 216-72 = 144. I did some rounding in calculating the volume of the cylinder, so it should not be exactly 144.

Answer 7

Thank you so much! That was the problem I've been stuck on since yesterday!

Answer 8

No problem. All these spatial geometry problems boil down to subtracting one value of the larger solid from the value of the smaller solid (i.e., area minus area, volume minus volume). They can be a bit daunting to visualize sometimes.